What do you call a movie taking place during the events of its previous movie?
It's Sidequel, as per Wikipedia:
A sidequel is a story which portrays events that occur at the same
time as the original work, but focuses on different characters in a
different setting. Such stories may intersect with the original work,
and often involve similar themes. One example is the video game Enter
the Matrix, which allows players to play out events that occurred in
parallel to those in the film The Matrix Reloaded. Another example
would be the George R. R. Martin novel A Storm of Swords, which was
published in two volumes, each volume describing events which take
place at the same time.
And what do you call a movie mix up of these kinds?
It's called Macroquel
A macroquel is a companion work that serves as prequel, interquel and
sequel to a previous work and covers events before, during, and after
the previous continuity. A notable example of this is 300: Rise of an
There is one more related term to it called : Paraquel
In a paraquel (parallel story), as with a prequel, the focus is not
only on the outcome but on the characters and previously unrevealed
information. The Gregory Maguire series (and later Broadway
musical) 'Wicked starts as a prequel and develops into a sidequel to
L. Frank Baum's book The Wonderful Wizard of Oz and its sequels.*
Note: Refer same Wikipedia link for other similar terms for *quels like Midquel, Interquel, and Pseudosequels.